A circle has radius 6. What is the area of a sector with a central angle of 150°?

The sector is $\frac{150}{360}=\frac{5}{12}$ of the circle. The circle's area is $\pi(6)^2=36\pi$, so the sector's area is $\frac{5}{12}\cdot36\pi=15\pi$, choice H. Choice J ($36\pi$) is the full circle. Choice G ($9\pi$) is a quarter of the circle, the sector for $90^\circ$. Choice F ($6\pi$) is one sixth of the circle, the sector for $60^\circ$. Since $150^\circ$ is a bit less than half the circle, the answer should be a bit less than $18\pi$, and $15\pi$ fits.